Singularities, Representation of Algebras, and Vector Bundles

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September 1987



It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.


Survey of vector bundles on curves.- Finite and countable CM-representation type.- Finite dimensional algebras and singularities.- Cohen-Macaulay modules on quadrics.- Monomial curves and obstructions on cyclic quotient singularities.- The Grothendieck group of invariant rings and of simple hypersurface singularities.- Torsionsfreie Moduln bei Deformation von Kurvensingularitäten.- Deformation of modules on curves and surfaces.- A characterisation of strictly unimodular plane curve singularities.- Polar curves, resolution of singularities and the filtered mixed hodge structure on the vanishing cohomology.- On the betti numbers of the milnor fibre of a certain class of hypersurface singularities.- Reflexive modules on cyclic quotient surface singularities.- Almost split sequences for ?-graded rings.- The auslander-reiten quiver of an isolated singularity.- A class of weighted projective curves arising in representation theory of finite dimensional algebras.- Repetitive categories.- Almost split sequences for some non-classical lattice categories.- Special instanton bundles and poncelet curves.- Groupe de picard des variétés de modules de faisceaux semi-stables sur ?2.- On the rationality of the moduli space for stable rank-2 vector bunoles on P2.- A theorem on zero schemes of sections in two-bundles over affine schemes with applications to set theoretic intersections.
EAN: 9783540182634
ISBN: 3540182632
Untertitel: Proceedings of a Symposium held in Lambrecht/Pfalz, Fed. Rep. of Germany, Dec. 13-17, 1985. 1987. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: September 1987
Seitenanzahl: 400 Seiten
Format: kartoniert
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